1. The problem asks us to classify the numbers 1, 6, 25, 29, 31, 33, 49, 51, and 53 into three categories: Prime, Composite, and Neither. 2. Definitions: - A **prime number** is a number greater than 1 that has exactly two distinct positive divisors: 1 and itself. - A **composite number** is a number greater than 1 that has more than two positive divisors. - The number 1 is **neither prime nor composite**. 3. Let's check each number: - 1: Neither prime nor composite. - 6: Divisors are 1, 2, 3, 6 (more than two), so composite. - 25: Divisors are 1, 5, 25 (more than two), so composite. - 29: Divisors are 1 and 29 only, so prime. - 31: Divisors are 1 and 31 only, so prime. - 33: Divisors are 1, 3, 11, 33 (more than two), so composite. - 49: Divisors are 1, 7, 49 (more than two), so composite. - 51: Divisors are 1, 3, 17, 51 (more than two), so composite. - 53: Divisors are 1 and 53 only, so prime. 4. Final classification: - Prime: 29, 31, 53 - Composite: 6, 25, 33, 49, 51 - Neither: 1 This completes the sorting of the numbers into the chart categories.